H13I-01
Parameter Estimation, Model Initialisation and Data Assimilation Issues for Distributed Flood Forecasting Models
Distributed hydrological models are receiving increasing attention for use in flood forecasting and warning. This in part reflects an operational demand to extend the areas receiving warnings and where, typically, there is an absence of local river gauging. Distributed modelling can offer an area-wide forecasting approach and is a natural way to proceed for flood warning at ungauged locations. The modelling can also benefit from improved spatial datasets on terrain, land cover, soil and geology properties together with space-time datasets of rainfall. Simple physical-conceptual distributed model formulations offer the prospect of linking the spatial datasets directly to model properties, leaving only a small number of regional parameters to calibrate using flows at gauged locations within the modelled domain. Initialisation of such distributed models presents new challenges in real-time situations where a long spin-up period is undesirable. The problem of initialisation is closely related to that of data assimilation where the aim is to increase forecast accuracy by updating the states of the distributed model in real-time. Approaches to these issues will be discussed in the context of ongoing work in the UK on improving flood forecasting and warning methodologies.
H13I-02
A new approach to the calibration of complex watershed models in ungauged basins using regionalized hydrologic indices
Hydrologic models are increasingly using more complex representations of watershed processes, which is reflected by the recent focus on spatially distributed models in the literature. Although these models seek to more realistically represent watersheds, many of their parameters cannot be estimated reliably from physical characteristics only, leading to uncertain priors and unreliable predictions if observations of the watershed response are not available for model conditioning. Large parts of the world, including most of the US river network, remain ungauged and alternative approaches to reduce a priori parameter uncertainty have to be found. Here we present a new approach based on the regionalization of streamflow characteristics in an uncertainty framework. A novel multi-objective formulation of the calibration problem allows for the use of powerful evolutionary algorithms to condition any watershed scale model on expected regionalized ranges of streamflow characteristics at ungauged locations. Our initial study using 30 UK watersheds shows that this approach results in reliable and sharp ensemble predictions, while the computational efficiency of the approach show its potential for application to complex spatially-distributed models. Global sensitivity analysis is used to analyze differences in the use of local and regional observations.
H13I-03
Calibrating a distributed hydrological model in a basin with heterogeneous geology
Calibrating distributed hydrological models is a challenging task because of the large number of model parameters (multiple model parameters for multiple sub-basins). A common approach is to apply a set of "parameter multipliers" to the model parameters in each sub-basin. This significantly reduces the dimensionality of the optimization problem, but can result in a spatial distribution of model parameters that is inconsistent with spatial differences in hydrological processes. More thoughtful calibration strategies are needed, especially in river basins where the geology is heterogeneous. This paper reports on our experience calibrating a distributed hydrological model for the Rangitaiki River basin in New Zealand. The Rangitaiki is an interesting river in that the geology of the western half of the river basin is pumice, which responds slowly to rain events; while the geology of the eastern half of the river basin is greywacke, which responds rapidly to rain events. Several different calibration strategies were tested, each of which modifies the frequency distribution that describes the a-priori parameters assigned to sub-catchments throughout the river basin. The spatial parameters are modified en masse, or modified in clusters according to geographic location or sub-catchment geology. Results show that spatial variability in model parameters is necessary to produce realistic streamflow simulations both at the basin outlet and at interior points in the basin. The required complexity of the calibration strategy depends on the reasonableness of a-priori parameter estimates—if a-priori model parameters are constant across all sub-catchments, then more complex calibration methods are needed to reproduce spatial variability in runoff responses. The results of the analysis are currently being used to design a methodology to estimate model parameters for all river basins throughout New Zealand.
H13I-04
Relationship Between Spatial Discretization and the Parameters and Model Performance of Precipitation-Runoff and Water Balance Models
The traditional approach in the application of precipitation-runoff or water balance models is to calibrate model parameters with observed input-output data. However, for the prediction in ungauged basins parameters have to be estimated a priori, for example from spatial data sets. Also for spatially distributed models, the a priori estimation of parameters using spatial data sets is desirable. In most studies to date, the spatial discretization of the model is not accounted for in the parameter estimation process. This study investigates the relationship between the spatial discretization, optimal parameter values, and the model performance. The results of precipitation-runoff and water balance modeling in several Austrian and US catchments will be presented. Models were applied repeatedly with varying spatial discretizations, from distributed to lumped, conducting a series of tests. The results show that the optimal values of some parameters are highly dependent on the spatial discretization, whereas other parameters are less sensitive. In general, the most sensitive parameters are ones that control highly threshold-like processes. Because of parameter interactions, the less sensitive parameters are also eventually affected by the spatial discretization. The model performance shows only little sensitivity to the spatial discretization, as long as model parameters are re-calibrated when moving from one spatial discretization to another. This has the consequence that the optimal parameters of lumped models have little correlation with their distributed counterparts, since the parameters have to overcome deficits in the spatial representation of threshold processes. Therefore, it is clear that these deficits need to be taken into account in any kind of a priori parameter estimation for lumped or semi-distributed models.
H13I-05
A Reduced Extended Kalman Filter Method For Data Assimilation And Parameter Optimization
This work is an extension of our two recent papers [Kao et al., Data assimilation with an extended Kalman filter for an impact-produced shock-wave study, J. Comp. Phys., 196 (2004), 705-723, and Kao et al., Estimating model parameters for an impact-produced shock-wave simulation: Optimal use of partial data with the extended Kalman filter, J. Comp. Phys., 214 (2006), 725-737 ] about the applications of the extended Kalman filter (EKF) to data assimilation in predictive codes. We have shown through the above two studies that the EKF method successfully estimates the evolving model state variables as well as model parameters of a shock-wave system by merging single-point pressure data into an Euler-equations computer code. We here intend to introduce a reduced EKF for the same purposes in terms of data assimilation and parameter optimization, but with a much smaller computational cost so that the applications of EKF to multi-dimensional realistic problems can be made possible. One of the distinctive features of EKF is that, as the system evolves forward in time, the EKF algorithm tracks the time-dependent error-covariance matrix of the model's state variables and parameters based on a consistent tangent-linear approximation of the model dynamics. When data becomes available at one instant in time, the update of the model state variables and parameters is achieved through a functional form of the linear merger of the model prediction and the data, subjective to the minimization of the trace of the error-covariance matrix of the model state variables and parameters. It, however, has been a concern that the calculation for the time evolution of the error-covariance matrix in applying EKF is computationally demanding and prohibitively expensive for real multi-dimensional problems. Several simplified approaches of EKF have been proposed to reduce the computational burden. This current study was actually motivated by Dee's work [Dee, P. D., 1991: Simplification of the Kalman filter for meteorological data assimilation. Q. J. Meteorol. Soc., 117, 365-384] and the results revealed in Evensen's study [Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods for forecast error statistics. J. Geophys. Res., 99, C5, 10143-10162]. In Kao et al. (2006), we were aware of that the errors associated with the model parameters are the main source of the total variances of the model state variables. Our simplification presented here somewhat resembles to the approach by Dee but takes it to an extreme by not considering the sensitivity due to the internal dynamics in the error propagation at all. Our method operates on the formalism in Kao et al. (2006) which is based upon an augmentation that the model parameters are treated as a part of the state variable vector, where the model parameters receive no influence from model dynamics and are only subject to a system error. The two groups within this augmented state vector would create four blocks in the error-covariance matrix among which a well-defined inter-relationship associated with error propagation can be derived. The test of the reduced EKF against the full EKF using the shock-wave model and cloud microphysics model will be presented. With cost effectiveness up to orders of magnitudes, the results are also satisfactory in terms of the assimilated field variables and optimized model parameters.
H13I-06
Efficient Parameter and State Estimation through Ensemble Kalman Filter and Discrete Cosine Parameterization with Application in Oil Reservoir Characterization
State and parameter estimation in large hydrocarbon reservoirs is challenging due to several reasons including: 1) Scarcity of available measurements relative to the number of unknowns, leading to an ill-posed inverse problem; 2) Computational effort required for large reservoir problems; 3) The need to insure that solutions are geologically realistic. All of these problems can be helped by using algorithms that rely on efficient and parsimonious descriptions (or parameterizations) of reservoir properties. This paper combines a novel state and parameter reduction approach, the discrete cosine transform, with a recursive estimation technique, the ensemble Kalman filter, to provide efficient estimation of uncertain states and petrophysical properties (parameters) in large reservoirs. The application and generality of this approach is demonstrated using two waterflooding experiments characterized by different types of geological variability.
H13I-07
Use of traditional and novel statistics to calibrate of hydrological model for TMDL analysis in the Calleguas Creek Watershedfor the TMDL analysis in the Calleguas Creek Watershed
A hydrologic model was developed using Hydrologic Simulation Program – Fortran (HSPF) for the Calleguas Creek Watershed (CCW) in Ventura County, Southern California, for flood control analysis. To provide decision support in total maximum daily load (TMDL) development, the model was expanded to simulate suspended sediment and particle associated and dissolved fractions of select metals and selenium all of which were also manually calibrated. A Pathogen TMDL is required for the CCW and it is desired to modify the available HSPF model of the watershed to simulate fate and transport of bacteria. Bacteria are difficult to measure and model and they can be attached to suspended sediment; thus, a detailed simulation of the sediment is required. For a Pathogen TMDL, it is commonly accepted that quantification of the uncertainty in the predictions is as or more important than the predicted value. In the present work, we decided to re-analyze the calibration of the hydrological model, and then add calibration of sediment and bacteria. The goal of the new model is to better match the low flow periods of record, sediment transport, and indicator bacteria than would be possible using the available model and hand calibration. The HSPF model was recalibrated using the automatic inversion code UCODE-2005. Furthermore, the utility of local sensitivity analysis, parameter-estimation using single objective-function optimization methods, and tests against new data to evaluate a fully distributed hydrological model are explored. The approach considered differs from other recent publications on analysis of hydrologic models in the weighting of observations based on an analysis of observation errors, the sensitivity analysis methods used, the single objective-function used for parameter estimation, and the combination of traditional and unusual (for hydrologic models) statistics considered to evaluate model fit. Traditional statistics, such as Nash and Sutcliffe coefficient, provide information on the overall result of the calibration and not on the single observation used. In the specific case, measures of leverage, Cook's D and DFBETAs, commonly used for groundwater models, are applied to the CCW hydrological model to evaluate the importance of the different hydrological observations used (here, daily values, monthly volumes and exceedance times) and to provide guidelines for the more complicated sediment and bacteria calibration.
H13I-08
Hierarchical and Adaptive Concepts in the Identification of Reaction Parameters in Multicomponent Reactive Transport Models
Recent challenges like bioremediation, longterm underground storage of reactive waste or underground carbondioxide sequestration require more and more complex multicomponent reactive transport models. Athough being demanding concerning their efficient numericical approximation, the decisive bottleneck in using such models seems to lie in the availability of the increasing range of reaction parameters entering such a model (Monod parameters in multplicative Monod models in conjunction with bioremediation, rate parameters in kinetic mass action law models, ...). We address the reliable and accurate identification of such parameters from one of most controlled experimental set ups, namely from soil column breakthrough curves (letting the upscaling issue aside), but the following methology can also applied to field experiments. It is wellknown that the (missing) sensitivity and the correlation of parameters prevent a reliable reconstruction from naive history matching (output least squares minimization). For a fixed experimental setup we propose a systematic use of the singular values of the sensitivity matrix in the definition of the error functional to design an adaptive approach in which after each termination in a (local) minimum the error functional is changed. Applications to the identification of Monod parameters show significant improvements in possible accuracy. Furthermore this approach is combined with a hierarchical concept to filter out the most sensitive parameters and identify them first. In a further step these approaches can be used also within experimental design to find more appropriate sequences of experiments which can be taken into account into an multiexperiment identification approach.